In the course of processing video data for display at a display device, image data representing an image frame is temporarily stored in a frame buffer. In an effort to reduce the frame buffer size and to reduce memory traffic due to read and write accesses to the frame buffer, the image data may be compressed when stored in the frame buffer. Arithmetic coding often is used to encode the uncompressed image data to generate compressed codewords, which are then stored in the frame buffer as a compressed version of the image data. Generally, the arithmetic coding process generates a codeword having two components: a fixed-length component that has the same number of bits regardless of the input data; and a variable-length component that has a variable number of bits depending on the input data. In conventional implementations, the codewords are simply concatenated together into a bit string for storage in the frame buffer such that the variable-length components and fixed-length components are interleaved. Accordingly, when decompressing the compressed data in the frame buffer, the decompression module parses the bit string to locate the first bit with a value of 0 (hereinafter, a “0 bit”) as the termination bit of a corresponding variable-length component, and thus identify the variable-length component as such. In many instances it may be desired to decode multiple codewords in one clock cycle, and thus the decompression module may look ahead in the bit string and flag upcoming 0 bits as termination bits. However, due to the interleaved nature of the fixed-length components and variable-length components, one or more of the flagged 0 bits actually may be bits from a fixed-length component rather than a termination bit of a variable-length component. To compensate for this, conventional decoding modules implement additional logic to identify and eliminate the inadvertent flagging of 0 bits of fixed-length components as termination bits of variable-length components of codewords. This additional logic increases the complexity, cost, and power consumption of the resulting decompression module.